It's not that they speak it too well to be their first language, it's that a lot of the idioms are from English. Things like "irreparably stuck," "image to follow," and "one needs a third attack" all hint that if English isn't rabbitmoon's first language, they've been speaking it a very long time.
Also, King Jelly gives a costume, not a pet. And, if I remember correctly, Simon's eye color changes after you click him but before he starts singing. Although I grant you, it is rather understated. I did the same thing with Li before finally figuring out I was supposed to Bind Song his stupid helmet, instead of just take it off with my hands like would make sense.